Streaked photoemission from nanostructured surfaces and nanoparticles by attosecond extreme ultraviolet pulses into an infrared (IR) or visible streaking pulse allows for sub-fs-resolution of the plasmonically enhanced streaking-pulse electric field. It thus holds promise for the time-resolved imaging of the dielectric response in and plasmonic fields near nanostructures. After calculating the plasmonic field induced by IR and visible streaking pulses in 10-to 200-nm diameter Au, Ag, and Cu nanospheres, we numerically simulated streaked photoelectron spectra within a quantum-mechanical model. Our spectra show significant oscillation-amplitude enhancements and phase shifts relative to calculations that neglect the induced plasmonic field. We trace these observable effects to the distinct dielectric properties of the three investigated metals, demonstrating the applicability of streaking spectroscopy to the element-specific investigation of induced time-dependent electric fields near nanoparticle surfaces.